MinT - Best Known (67, 67+44, s)-Nets in Base 5

Best Known (67, 67+44, s)-Nets in Base 5

(67, 67+44, 252)-Net over F₅ — Constructive and digital

Digital (67, 111, 252)-net over F₅, using

3 times m-reduction [i] based on digital (67, 114, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 57, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(67, 67+44, 257)-Net over F₅ — Digital

Digital (67, 111, 257)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+44, 7594)-Net in Base 5 — Upper bound on s

There is no (67, 111, 7595)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385705 550945 299493 326079 846040 601195 027031 185935 218447 305788 377335 080420 905385 > 5¹¹¹ [i]